Question: Solve for $x$ and $y$ using elimination. ${2x+5y = 26}$ ${-2x+4y = -8}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $2x$ and $-2x$ cancel out. $9y = 18$ $\dfrac{9y}{{9}} = \dfrac{18}{{9}}$ ${y = 2}$ Now that you know ${y = 2}$ , plug it back into $\thinspace {2x+5y = 26}\thinspace$ to find $x$ ${2x + 5}{(2)}{= 26}$ $2x+10 = 26$ $2x+10{-10} = 26{-10}$ $2x = 16$ $\dfrac{2x}{{2}} = \dfrac{16}{{2}}$ ${x = 8}$ You can also plug ${y = 2}$ into $\thinspace {-2x+4y = -8}\thinspace$ and get the same answer for $x$ : ${-2x + 4}{(2)}{= -8}$ ${x = 8}$